By the way, there’s an interesting observation: my probability estimate before a coin toss is an objective probability that describes the property of the coin.
Don’t say “objective probability”—it’s a road straight to confusion. Probabilities represent your knowledge state. Before the coin is tossed you are indifferent between two states of the coin, and therefore have 1⁄2 credence.
After the coin is tossed, if you’ve observed the outcome, you get 1 credence, if you received some circumstantial evidence, you update based on it, and if you didn’t observe anything relevant, you keep your initial credence.
The obvious question is: can Sleeping Beauty update her credence before learning that it is Monday?
If she observes some event that is more likely to happen in the iterations of the experiment where the coin is Tails than in an iterations of the experiment where the coin is Heads than she lawfully can update her credence.
As the conditions of the experiment restrict it—she, threfore, doesn’t update.
And of course, she shouldn’t update, upon learning that it’s Monday either. After all, Monday awakening happens with 100% probability on both Heads and Tails outcomes of the coin toss.
I think that what I call ’objective probability” represent physical property of the coin before the toss, and also that before the toss I can’t get any evidence about the result the toss. In MWI it would be mean split of timelines. While it is numerically equal to credence about a concrete toss result, there is a difference and SB can be used to illustrate it.
Don’t say “objective probability”—it’s a road straight to confusion. Probabilities represent your knowledge state. Before the coin is tossed you are indifferent between two states of the coin, and therefore have 1⁄2 credence.
After the coin is tossed, if you’ve observed the outcome, you get 1 credence, if you received some circumstantial evidence, you update based on it, and if you didn’t observe anything relevant, you keep your initial credence.
If she observes some event that is more likely to happen in the iterations of the experiment where the coin is Tails than in an iterations of the experiment where the coin is Heads than she lawfully can update her credence.
As the conditions of the experiment restrict it—she, threfore, doesn’t update.
And of course, she shouldn’t update, upon learning that it’s Monday either. After all, Monday awakening happens with 100% probability on both Heads and Tails outcomes of the coin toss.
I think that what I call ’objective probability” represent physical property of the coin before the toss, and also that before the toss I can’t get any evidence about the result the toss. In MWI it would be mean split of timelines. While it is numerically equal to credence about a concrete toss result, there is a difference and SB can be used to illustrate it.